About

Welcome to the website of the project "Axiomatizing Metatheory - Frege's New Science", an FWF-funded research project that aims to re-evaluate some of the lesser-known aspects of the so-called Frege-Hilbert controversy (Project number: P 30448). The project has a specific focus on a proposal made by Frege where he claims that a "new science" has to be devised in order to study metatheoretical questions such as the consistency and mutual independence of axioms. The main aims of the project are

  • to make clear what Frege's New Science is supposed to look like exactly and how it relates to concepts and methods in modern and pre-modern mathematical logic.
  • to clarify Frege's motivation for introducing a New Science in the first place, and what his proposal implies for his philosophy of logic and mathematics.
  • to determine whether, and, if so, to what extent, Frege's conception of metatheoretical investigations might be reflected in contemporary discussions in the philosophy of logic.
The project runs from August 2017 to July 2020 and is led by Dr. Günther Eder as the principal investigator.

Project Description

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Publications


Published

  • Frege and the Origins of Model Theory in Nineteenth Century Geometry, Synthese (2019), https://doi.org/10.1007/s11229-019-02421-4.
    Abstract Full Text
  • Truth, Paradox, and the Procedural Conception of Fregean Sense, Philosophy of Logic and Mathematics: Proceedings of the 41st International Wittgenstein Symposium, Berlin/Boston: DeGruyter, 153-168 (2019).
    Abstract
  • Hilbert, Duality, and the Geometrical Roots of Model Theory (with Georg Schiemer), Review of Symbolic Logic, 11 (1), 48-86 (2018).
    Abstract Full Text

Under Review

  • Projective Duality and the Rise of Modern Logic
  • Frege on Objecthood and Intuition in Projective Geometry

In Preparation

  • A Formal Reconstruction of (Blanchette's Reading of) Fregean Provability
  • Meaning, Truth, and Paradox

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Talks


Upcoming

Past

  • 07/2019, Do any two lines meet in a point? Frege on (projective) Geometry. 2nd Prague Workshop on Frege's Logic, Institute of Philosophy, AKC, Prague.
  • 02/2019, Meaning, Truth, and Paradox. Annual Conference of the Israeli Philosophical Association, Bar-Ilan University, Ramat Gan.
  • 03/2019, Frege and Semantics. FregeFest VI, UC Irvine.
  • 08/2018, Truth, Paradox, and the Procedural Conception of Fregean Sense. 41st International Wittgenstein Symposium, Kirchberg.
  • 05/2018, The Procedural Conception of Fregean Sense. Work-in-Progress Seminar of the Department of Philosophy (KGW), Salzburg.
  • 02/2018, Frege, Hilbert, and the Origins of Model Theory in 19th Century Geometry. Workshop Modern Axiomatics and Early Metatheory, Vienna.

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Events



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